Topic

Sequential Information Design

Abstract

The literature on implementation has focused mainly on cases in which
agents have both agency over their actions and over the time at which they
commit to their actions. We take as given the set of agents, their set of actions,
and their payoffs. We ask what distributions over actions are consistent
with the players playing according to some extensive form. The main
result of the paper is to show that a distribution over outcomes is implementable
as a Perfect Bayesian equilibrium (PBE) of an admissible extensive
form if, and only if, it is implementable as a PBE of a canonical extensive
form. The latter is an admissible extensive form, in which there is a randomization
device that not only sends (private) recommendations to the agents,
but also selects the order in which the agents move; moreover, subsequent
recommendations can be made conditional on actions already taken. This
result strictly generalizes Aumann’s notion of correlated equilibrium, and
Bergemann and Morris’ notion of Bayes’ correlated equilibrium.